Quantum Physics

   

A Simple Quantum Algorithm for Exponentially Fast Target Searching in the Unstructured Database

Authors: Dhananjay P. Mehendale

We present an exponentially fast simple quantum algorithm to run on a quantum computer for searching the unknown target in the unstructured database. This algorithm provides an eloquent example that clearly demonstrates the enormous advantage of quantum parallalism. This novel quantum algorithm is based on the idea of simultaneously utilising $(n/2)$ oracles or black-box functions followed by $(n/2)$ diffusion transforms for searching target in the unordered data set of size $N = 2^n.$ We show that we can attain the (explicitly unknown) target in the unstructured database of size $N = 2^n$ by giving only one call, simultaneously (parallely) and independently, to just $(n/2)$ oracles or black-box functions followed by $(n/2)$ diffusion transforms that we define and implement using a quantum computer. This algorithm thus demonstrates the exponential speedup that can be achieved in obtaining the desired target from unstructed data set of size $N = 2^n$ which is indeed amazing! For a typical $NP-$complete problem in which one has to find an assignment of one of some $b$ values to each of some $m$ variables, the number of candidate solutions, $N = b^m,$ grows exponentially with $m.$ Hence a classical exhaustive algorithm would take $O(b^m)$ operations, Grover's quantum algorithm would take $O(b^{m/2})$ operations, while the algorithm that we propose in this paper does this job in just a single operation!! Thus, using our quantum algorithm on a quantum computer one can establish the validity of $NP = P$ through a quantum mechanical procedure run on a quantum computer!!

Comments: 11 Pages.

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Submission history

[v1] 2017-02-01 11:57:13

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